For the subspace below, find a basis 12a +24b - 4c 1 9a - 3b - 3c :a, b, c in R -6a +5b +2c -3a +b +c a. (9,3, - 6,3), (– 4, - 3,2,1) b. (9,-3,- 3,0), (8, – 1,5, – 1) (12,9, – 6, – 4), -6,5,2,0) (12,9, – 6,– 3), (24, – 3,5,1) C. d. e. (12,9,–6,- 3), (24, - 3, - 3,1)

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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linear algebra hw, please label and answer. thank you!

For the subspace below, find a basis
12a +24b - 4c 1
9a - 3b -3c
:a, b, c in R
-6a +5b +2c
-3a +b+ c
(9,3,-6,3), (- 4, -3,2,1)
(9, – 3, – 3,0), (8,- 1,5, – 1)
(12,9,– 6,– 4), -6,5,2,0)
(12,9,– 6,-3), (24,– 3,5,1)
e. (12,9,–6,– 3), (24, – 3, – 3,1)
a.
b.
с.
d.
е.
Transcribed Image Text:For the subspace below, find a basis 12a +24b - 4c 1 9a - 3b -3c :a, b, c in R -6a +5b +2c -3a +b+ c (9,3,-6,3), (- 4, -3,2,1) (9, – 3, – 3,0), (8,- 1,5, – 1) (12,9,– 6,– 4), -6,5,2,0) (12,9,– 6,-3), (24,– 3,5,1) e. (12,9,–6,– 3), (24, – 3, – 3,1) a. b. с. d. е.
In P find the change-of-coordinates matrices from basis B to basis C.
B=(1+2t+2t?, 2– 3t + t?, 1-2t+4t²), C=(1, t, t²)
[1 2 1
2 2 -1
1
7 -3 -1
2 7 1]
1
2-3 -4
1 2
1
a.
b.
2 -3 1
C.
d.
2 -3 -2
|1 -4 7 -
1 -2 4
-1 -1 7
1 1 4
Transcribed Image Text:In P find the change-of-coordinates matrices from basis B to basis C. B=(1+2t+2t?, 2– 3t + t?, 1-2t+4t²), C=(1, t, t²) [1 2 1 2 2 -1 1 7 -3 -1 2 7 1] 1 2-3 -4 1 2 1 a. b. 2 -3 1 C. d. 2 -3 -2 |1 -4 7 - 1 -2 4 -1 -1 7 1 1 4
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